STUDENT NAME & ID : Omar Elalem (8937288)

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import seaborn as sns
import plotly
import plotly.express as px
import sklearn
from sklearn import datasets
plotly.offline.init_notebook_mode()
sns.set_style("whitegrid")

Load dataset from Sklearn

diabData = datasets.load_diabetes()

print(diabData["DESCR"])

.. _diabetes_dataset:

Diabetes dataset
----------------

Ten baseline variables, age, sex, body mass index, average blood
pressure, and six blood serum measurements were obtained for each of n =
442 diabetes patients, as well as the response of interest, a
quantitative measure of disease progression one year after baseline.

**Data Set Characteristics:**

  :Number of Instances: 442

  :Number of Attributes: First 10 columns are numeric predictive values

  :Target: Column 11 is a quantitative measure of disease progression one year after baseline

  :Attribute Information:
      - age     age in years
      - sex
      - bmi     body mass index
      - bp      average blood pressure
      - s1      tc, total serum cholesterol
      - s2      ldl, low-density lipoproteins
      - s3      hdl, high-density lipoproteins
      - s4      tch, total cholesterol / HDL
      - s5      ltg, possibly log of serum triglycerides level
      - s6      glu, blood sugar level

Note: Each of these 10 feature variables have been mean centered and scaled by the standard deviation times `n_samples` (i.e. the sum of squares of each column totals 1).

Source URL:
https://www4.stat.ncsu.edu/~boos/var.select/diabetes.html

For more information see:
Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani (2004) "Least Angle Regression," Annals of Statistics (with discussion), 407-499.
(https://web.stanford.edu/~hastie/Papers/LARS/LeastAngle_2002.pdf)

list(diabData)

['data',
 'target',
 'frame',
 'DESCR',
 'feature_names',
 'data_filename',
 'target_filename']

dataframe

df =pd.DataFrame(diabData["data"], columns= diabData["feature_names"])
df

	age	sex	bmi	bp	s1	s2	s3	s4	s5	s6
0	0.038076	0.050680	0.061696	0.021872	-0.044223	-0.034821	-0.043401	-0.002592	0.019908	-0.017646
1	-0.001882	-0.044642	-0.051474	-0.026328	-0.008449	-0.019163	0.074412	-0.039493	-0.068330	-0.092204
2	0.085299	0.050680	0.044451	-0.005671	-0.045599	-0.034194	-0.032356	-0.002592	0.002864	-0.025930
3	-0.089063	-0.044642	-0.011595	-0.036656	0.012191	0.024991	-0.036038	0.034309	0.022692	-0.009362
4	0.005383	-0.044642	-0.036385	0.021872	0.003935	0.015596	0.008142	-0.002592	-0.031991	-0.046641
...	...	...	...	...	...	...	...	...	...	...
437	0.041708	0.050680	0.019662	0.059744	-0.005697	-0.002566	-0.028674	-0.002592	0.031193	0.007207
438	-0.005515	0.050680	-0.015906	-0.067642	0.049341	0.079165	-0.028674	0.034309	-0.018118	0.044485
439	0.041708	0.050680	-0.015906	0.017282	-0.037344	-0.013840	-0.024993	-0.011080	-0.046879	0.015491
440	-0.045472	-0.044642	0.039062	0.001215	0.016318	0.015283	-0.028674	0.026560	0.044528	-0.025930
441	-0.045472	-0.044642	-0.073030	-0.081414	0.083740	0.027809	0.173816	-0.039493	-0.004220	0.003064

442 rows × 10 columns

Adding target data to the dataframe

df["target"] = diabData["target"]
df

	age	sex	bmi	bp	s1	s2	s3	s4	s5	s6	target
0	0.038076	0.050680	0.061696	0.021872	-0.044223	-0.034821	-0.043401	-0.002592	0.019908	-0.017646	151.0
1	-0.001882	-0.044642	-0.051474	-0.026328	-0.008449	-0.019163	0.074412	-0.039493	-0.068330	-0.092204	75.0
2	0.085299	0.050680	0.044451	-0.005671	-0.045599	-0.034194	-0.032356	-0.002592	0.002864	-0.025930	141.0
3	-0.089063	-0.044642	-0.011595	-0.036656	0.012191	0.024991	-0.036038	0.034309	0.022692	-0.009362	206.0
4	0.005383	-0.044642	-0.036385	0.021872	0.003935	0.015596	0.008142	-0.002592	-0.031991	-0.046641	135.0
...	...	...	...	...	...	...	...	...	...	...	...
437	0.041708	0.050680	0.019662	0.059744	-0.005697	-0.002566	-0.028674	-0.002592	0.031193	0.007207	178.0
438	-0.005515	0.050680	-0.015906	-0.067642	0.049341	0.079165	-0.028674	0.034309	-0.018118	0.044485	104.0
439	0.041708	0.050680	-0.015906	0.017282	-0.037344	-0.013840	-0.024993	-0.011080	-0.046879	0.015491	132.0
440	-0.045472	-0.044642	0.039062	0.001215	0.016318	0.015283	-0.028674	0.026560	0.044528	-0.025930	220.0
441	-0.045472	-0.044642	-0.073030	-0.081414	0.083740	0.027809	0.173816	-0.039493	-0.004220	0.003064	57.0

442 rows × 11 columns

plt.figure(figsize=(7,6))
plt.scatter(df["bmi"],  y=df["target"])
plt.xlabel("bmi")
plt.ylabel("target")
plt.title(f"Train Data:  442 data points, generated around a line with some noise")
plt.show()

x = df.iloc[:,:-1]
x

	age	sex	bmi	bp	s1	s2	s3	s4	s5	s6
0	0.038076	0.050680	0.061696	0.021872	-0.044223	-0.034821	-0.043401	-0.002592	0.019908	-0.017646
1	-0.001882	-0.044642	-0.051474	-0.026328	-0.008449	-0.019163	0.074412	-0.039493	-0.068330	-0.092204
2	0.085299	0.050680	0.044451	-0.005671	-0.045599	-0.034194	-0.032356	-0.002592	0.002864	-0.025930
3	-0.089063	-0.044642	-0.011595	-0.036656	0.012191	0.024991	-0.036038	0.034309	0.022692	-0.009362
4	0.005383	-0.044642	-0.036385	0.021872	0.003935	0.015596	0.008142	-0.002592	-0.031991	-0.046641
...	...	...	...	...	...	...	...	...	...	...
437	0.041708	0.050680	0.019662	0.059744	-0.005697	-0.002566	-0.028674	-0.002592	0.031193	0.007207
438	-0.005515	0.050680	-0.015906	-0.067642	0.049341	0.079165	-0.028674	0.034309	-0.018118	0.044485
439	0.041708	0.050680	-0.015906	0.017282	-0.037344	-0.013840	-0.024993	-0.011080	-0.046879	0.015491
440	-0.045472	-0.044642	0.039062	0.001215	0.016318	0.015283	-0.028674	0.026560	0.044528	-0.025930
441	-0.045472	-0.044642	-0.073030	-0.081414	0.083740	0.027809	0.173816	-0.039493	-0.004220	0.003064

442 rows × 10 columns

y = df["target"]
y

0      151.0
1       75.0
2      141.0
3      206.0
4      135.0
       ...  
437    178.0
438    104.0
439    132.0
440    220.0
441     57.0
Name: target, Length: 442, dtype: float64

from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn import linear_model
from sklearn import metrics
x_train,x_test,y_train,y_test = train_test_split(x,y,test_size = 0.2,random_state = 2)

reg = LinearRegression().fit(x_train,y_train)

y_test_pred = reg.predict(x_test)
print(y_test_pred)

[154.1235067  204.81721599 124.92988001 106.09339576 258.53035681
 256.32953702 118.75258786 119.52147402 101.50717468 190.54137158
 141.70360267 172.51631204 174.34089304 134.81184017 294.13950798
  94.11403289 211.97052873 156.49984762 134.20709632 119.62534726
 148.88045343 165.00378118 151.09977307 176.03719872 133.27651748
 221.29531227 197.17482787  96.15923158  50.26531577 230.48342249
 242.06266394 114.1153262   67.0785352   94.53179042 201.21593262
 167.05306138 159.87838519 192.78601513 114.49291816 233.4825497
 140.82309666 121.06814332 192.27431013 191.13157307 179.1698153
 148.35140027 163.47610288 276.81203359 100.17813072 164.11265163
 255.81074398 136.94979051 152.37507828 107.92662528 194.21661635
  77.35015426 118.50951725  68.38527563 154.29094022 162.48905632
 168.36590928 156.8764705   97.13958436 238.17121803 145.46093854
 117.65678691 168.88768692 198.38893625 118.24408332 124.64831033
 223.17842907 200.62634508 129.54591274 158.1553552  154.33593871
 114.47109854  70.4524892   76.39237963 172.41319558  80.56189628
  80.27309695  89.46135201 186.21265361 275.46607679 208.26816596
 143.7962915  291.28438095 206.32601303  94.22801028]

print(" The intercept is ", reg.intercept_)
print("The  slope is ", reg.coef_)
print("The score of train data set ", reg.score(x_train,y_train)*100)
print("The score of test data set ", reg.score(x_test,y_test)*100)

 The intercept is  151.88334520854633
The  slope is  [  -9.16088483 -205.46225988  516.68462383  340.62734108 -895.54360867
  561.21453306  153.88478595  126.73431596  861.12139955   52.41982836]
The score of train data set  53.23676737904685
The score of test data set  43.99387660024645

print(" Mean Absloute Error ",metrics.mean_absolute_error(y_test,y_test_pred))
print("Mean Square Error ",metrics.mean_squared_error(y_test,y_test_pred))

 Mean Absloute Error  45.21292481299676
Mean Square Error  3094.4295991207023

plt.figure(figsize=(8, 8))
plt.scatter(y_test, y_test_pred)
plt.plot(y_test, y_test, color='r')
plt.title('Actual VS Predicted Values')
plt.xlabel('Actaul')
plt.ylabel('Predicted')
plt.show()

plt.figure(figsize=(8,8))
arj = sns.heatmap(df.corr(),annot= True)

conclusion from data set :

-) I believe linear regression is not the best option for this model because the training data is too dispersed and the correlation between BMI and disease progression is normal correlation.

-) We can also see from the loss function that our mean absolute error is high, which indicates that the model is not operating correctly and that the forecasts are far from the actual values,according to a high MAE.